For a reaction, `E_(a)= 0 and k= 3.2xx10^(4)s^(-1)` at `300 K`. The value of `k` at `310 K` would be

Options

A. `6.4xx10^(4)s^(-1)`
B. `3.2xx10^(8)s^(-1)`
C. `3.2xx10^(4)s^(-1)`
D. `3.2xx10^(5)s^(-1)`

Explanation

To solve the problem, we need to determine the value of the rate constant \( k \) at \( 310 \, K \) given that the activation energy \( E_a = 0 \) and the rate constant \( k = 3.2 \times 10^4 \, s^{-1} \) at \( 300 \, K \).

### Step-by-Step Solution:

1. **Understand the Arrhenius Equation**:
The Arrhenius equation relates the rate constant \( k \) to the temperature \( T \) and activation energy \( E_a \):
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = pre-exponential factor (Arrhenius constant)
- \( E_a \) = activation energy
- \( R \) = universal gas constant (approximately \( 8.314 \, J \, mol^{-1} \, K^{-1} \))
- \( T \) = temperature in Kelvin

2. **Substituting the Given Values**:
Since \( E_a = 0 \), we can simplify the equation:
\[ k = A e^{-\frac{0}{RT}} = A e^{0} = A \]
This means that when \( E_a = 0 \), the rate constant \( k \) is equal to the pre-exponential factor \( A \) and is independent of temperature.

3. **Determine the Rate Constant at 310 K**:
Given that \( k = 3.2 \times 10^4 \, s^{-1} \) at \( 300 \, K \), and since \( k \) does not change with temperature when \( E_a = 0 \), we can conclude:
\[ k_{310 \, K} = k_{300 \, K} = 3.2 \times 10^4 \, s^{-1} \]

4. **Final Answer**:
Therefore, the value of \( k \) at \( 310 \, K \) is:
\[ k_{310 \, K} = 3.2 \times 10^4 \, s^{-1} \]

### Conclusion:
The value of \( k \) at \( 310 \, K \) is \( 3.2 \times 10^4 \, s^{-1} \).